Some new near-normal sequences
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Publication:3073929
zbMATH Open1205.05031arXiv0907.3129MaRDI QIDQ3073929
Publication date: 11 February 2011
Abstract: The normal sequences NS(n) and near-normal sequences NN(n) play an important role in the construction of orthogonal designs and Hadamard matrices. They can be identified with certain base sequences (A;B;C;D), where A and B have length n+1 and C and D length n. C.H. Yang conjectured that near-normal sequences exist for all even n. While this has been confirmed for n not exceeding 30, so far nothing else was known for larger n. We show that NN(32) consists of 8 equivalence classes and we exhibit their representatives. We also construct representatives for two equivalence classes of NN(34). On the other hand our exhaustive computer searches show that NS(31) and NS(33) are void.
Full work available at URL: https://arxiv.org/abs/0907.3129
Hadamard matricesbase sequencesYang numbersGoethals-Seidel arraynormal and near-normal sequences\(T \)-sequences
Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Other designs, configurations (05B30)
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